Solidify thickness doesn't correspond to specified scale although scale of object is applied
Immediately after posting this question, I realised my problem.
Hopefully it might help someone else, in the future (or in the past)

The object was parented to a dummy object (this project is full of it, I think I didn't import this drawing the right way), which wasn't scaled properly, affecting the scale of the child-object.

I remember now that it appeared strange to me that the object (a technical drawing of a MAN NG272 Public Transport Bus, wasn't scaled properly, 
but as an afterthought I think it was, but the empty (empties) wasn't (weren't).

So, instead of removing the dummy parents, I just scaled the whole drawing  to what I thought was right, hence a number of problems later on ...

So the actual solution was to remove the parent of the object, keeping the transform (Alt-P) and then re-apply the scale, after which the solidify parameter works as expected.